# Efficiently Generating Correlated Sample Paths from Multi-step Time Series Foundation Models

arXiv: https://arxiv.org/abs/2510.02224 · HTML: https://mlsanity.com/paper/2510.02224/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 19 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [The pitfalls of next-token prediction](https://mlsanity.com/paper/2403.06963/) (2024)
- [TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning](https://mlsanity.com/paper/2505.23719/) (2025)
- [From Tables to Time: Extending TabPFN-v2 to Time Series Forecasting](https://mlsanity.com/paper/2501.02945/) (2025)
- [TACTiS: Transformer-Attentional Copulas for Time Series](https://mlsanity.com/paper/2202.03528/) (2022)
- [Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting](https://mlsanity.com/paper/2111.06581/) (2021)
- [From Predictions to Decisions: The Importance of Joint Predictive Distributions](https://mlsanity.com/paper/2107.09224/) (2021)
- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Deep Generative Quantile-Copula Models for Probabilistic Forecasting](https://mlsanity.com/paper/1907.10697/) (2019)
- [On Simulation and Trajectory Prediction with Gaussian Process Dynamics](https://mlsanity.com/paper/1912.10900/) (2019)
- [Weather-Informed Probabilistic Forecasting and Scenario Generation in Power Systems](https://mlsanity.com/paper/2409.07637/) (2024)
- [Multivariate Forecasting Evaluation: On Sensitive and Strictly Proper Scoring Rules](https://mlsanity.com/paper/1910.07325/) (2019)

## Built on by (most cited first, 4 of 4)

- [Post-Training in Time Series Foundation Models: A Unifying Framework](https://mlsanity.com/paper/2607.20002/) (2026)
- [Signature-Kernel Based Evaluation Metrics for Robust Probabilistic and Tail-Event Forecasting](https://mlsanity.com/paper/2602.10182/) (2026)
- [Interweaving Marginals into Multivariate Sample Paths: Training-Free Dependence Construction for Probabilistic Time Series Foundation Models](https://mlsanity.com/paper/2609.25980/) (2026)
- [A Hierarchy of Entropy-Shapley Games for Multivariate Predictive Uncertainty](https://mlsanity.com/paper/2609.35217/) (2026)

## Abstract (arXiv)

Many time series applications require access to multi-step forecast trajectories in the form of sample paths. Recently, time series foundation models have leveraged multi-step lookahead predictions to improve the quality and efficiency of multi-step forecasts. However, these models only predict independent marginal distributions for each time step, rather than a full joint predictive distribution. To generate forecast sample paths with realistic correlation structures, one typically resorts to autoregressive sampling, which can be extremely expensive. In this paper, we present a copula-based approach to efficiently generate accurate, correlated sample paths from existing multi-step time series foundation models in one forward pass. Our copula-based approach generates correlated sample paths orders of magnitude faster than autoregressive sampling, and it yields improved sample path quality by mitigating the snowballing error phenomenon.